The waiters were serving borscht and blinis while we sat at our tables in the faux-Russian supper club, waiting for the show to start the other night. A sociable young women in 19th-century period dress stopped by to welcome us and asked if we had everything we needed. As long as you asked, I said, my friend here ordered a vodka a half-hour ago, and it still hasn’t arrived. Her pretty face grew clouded; she said she’d look into it, but quickly had to scoot away. The music had struck up, and she was a key part of the opening number. I was complaining about the service to one of the stars of the show.

“Immersive” theater is all the rage these days. No longer can audiences sink into their seats and be assured of an uninterrupted couple of hours of passive entertainment (or snoozing). More and more shows are “immersing” the audience in the action. At the hit off-Broadway show Sleep No More, the audience wends its way through a dilapidated hotel, having random encounters with actors miming snatches of scenes from Macbeth. Even in conventional Broadway theaters, audience members are apt to be called up onstage by Bette Midler (playing pushy Hollywood agent Sue Mengers in I’ll Eat You Last) or invited to wander onto the stage before the show, to explore the set or belly up to the bar, as in the Tony-winning musical Once.

Some of this is just gimmickry. But two new immersive off-Broadway musicals use the technique to wonderfully energizing effect. In Here Lies Love, David Byrne’s almost shamefully enjoyable new show about the rise and fall of Filipino First Lady Imelda Marcos, the audience stands on a disco floor for the entire 90 minutes, as the sung-through show is performed on a series of moving stages. In Natasha, Pierre and the Great Comet of 1812, characters from Tolstoy’s War and Peace come to life in a Russian cabaret. The audience gets to sit through this one (and even eat dinner), but the actors can pop up anywhere — on the ribbon-like stages that snake around the dining area, in between the tables, or even right in your lap.

Turning War and Peace into a musical is a stage challenge, to say the least, and Natasha, Pierre is amusingly self-aware of that. The opening number introduces us to the major characters with jaunty, tongue-in-cheek directness (“Anatole’s hot, Helene’s a slut, Sonya’s good…”). Later, to set up a series of epistolary exchanges, the cast sings, with a wry wink: “In 19th-century Russia/ We write letters, we write letters/ We put down in writing / What is happening in our minds…” But the show actually takes its narrative task seriously, even as it mashes Tolstoy’s mammoth saga down to a Masterpiece Theater soap opera, centered on the naïve provincial girl Natasha’s introduction to Moscow society in Napoleon-era Russia.

Pierre, the moody malcontent who provides the novel’s philosophical core, mostly seems like a distraction here. But as played by the show’s lyricist-composer-author Dave Malloy, he gives the musical its raspy rock soul. The rest of his winning score is a mix of Russian folk music, Chess-era theater-pop, with a bit of of country and Sondheim thrown in for good measure. All of which goes down very easily in the luxe setting (red velvet curtains, framed paintings) and guided by Rachel Chavkin’s playfully intrusive staging, which gives every patron a front-row seat.

Here Lies Love is even more aggressive in getting the audience involved. A troupe of ushers keep the crowd revved up by leading them in dance moves, and herding them around the floor to make way for the shape-shifting stages. And yet, as in Natasha, Pierre, the show takes its storytelling duties seriously, as it chronicles the rise of Imelda (the excellent Ruthie Ann Miles) from poor country girl to wife of brutal dictator Ferdinand Marcos, with a digression to her early romance with Ninoy Aquino, who becomes her chief political adversary.

The sprawling narrative (political corruption, marital problems, the People’s Revolution) has more sweep than depth. But Alex Timbers’ creative staging — which features a DJ, video projections, newsreel footage and a band of versatile backup singers — keeps our heads spinning, if only to figure out which end of the auditorium the miked voices are coming from.

But Here Lies Love — which like Evita, the show to which it bears obvious similarities, began as a concept album — is mainly about the music. Rock pioneer Byrne, working with Fatboy Slim, has simply created one of the best theater scores of recent years. It combines infectious Latin, African and disco beats with lovely melodies that seem both distinctive yet instantly familiar: Imelda’s needy but defiant cry to her people, “Why Don’t You Love Me?”: the haunting “Order 1081”; the irresistible, anthemic title tune, “Here Lies Love.”

It’s the sort of rich, but seemingly effortless score that gives you fresh hope for the possibilities of musical theater — an elixir for an often stodgy and derivative form. Call it total immersion therapy.

Richard, are you missing something? Natasha, one of the best shows? Did you watch Murder Ballad Musical? That is the best show. You need to be more thorough if you are going to comment on best shows. You should check out Murder Ballad Musical at Union Square and update your review.